Is data-efficient learning feasible with quantum models?

Abstract

The importance of analyzing nontrivial datasets when testing quantum machine learning (QML) models is becoming increasingly prominent in literature, yet a cohesive framework for understanding dataset characteristics remains elusive. In this work, we introduce a data-generation tool that allows to construct semi-artificial classical datasets tailored to quantum kernel methods (QKMs). Using this tool, we show that on fully classical datasets, QKMs can require fewer training examples than classical kernels to reach comparable error, providing clear empirical evidence that data-efficient learning with quantum models is possible on classical data. The main motivation behind this tool is to enable the community to perform controlled studies to figure out which dataset characteristics are particularly fitting for quantum models by tuning the data-generation procedure. Additionally, our study brings a spectral-bias-based generalization metric from classical kernel methods into the QML domain and show that the performance predicted by this metric aligns closely with empirical results, thereby closing an important gap between theory and practice in QML generalization. Our tool paves the way for a systematic exploration of dataset complexities. This could potentially contribute to a deeper understanding of the generalization benefits of QKM models (extendable to a broader family of QML models) and shifts the search for quantum advantage from ad hoc benchmark hunting to principled dataset design.